An insurance company has an online help service for its customers. Customer queries that take more than 5 minutes to resolve are categorized as “unsatisfactory” experiences. To evaluate the quality of its service, the company takes 10 samples of 100 calls each while the process is under control. The resulting p values are as follows:
p VALUES (n = 100)
0.08
0.11
0.12
0.06
0.13
0.09
0.16
0.09
0.18
0.15
a. Calculate the p and Sp values and set up control limits so that future sample p values should fall within the control limits 99.7% of the time.
b. Suppose the insurance company takes four additional samples, yielding the following p values: 0.9, 0.12, 0.25, and 0.10. Plot the results and circle all values which suggest that the process is "out of control." Is it possible that a sample result could fall outside the control limits due to pure chance? Explain.
c. Now suppose that the sample size is actually 50, not 100. Recalculate the control limits for the p chart. What happened? Explain.